regex.bend source
regex.bend on the hub · documented module
# Linear-time regular expressions: RE2 syntax, Pike VM, capture groups. Source: https://github.com/paymog/bend-kit/tree/main/regeximport Baseimport 0x6c784a08486e2e02415e89c5249e9e8a/unicode.bend as U# Positions count code points of the String, not octets.# Leftmost-first semantics, as RE2 and Perl: the first alternative that matches wins.# Syntax# ------# A set member: a code point range, or a Unicode general category ("L", "Lu", ...).type Item is Data: Rng{lo: U32, hi: U32} Prop{neg: Bool, name: String}# Assertion kinds: 0 start of text, 1 end of text, 2 word boundary, 3 not a word boundary.type Node is Data: NEmpty{} NSet{neg: Bool, items: List<&2, Item>} NAssert{k: U32} NCat{a: Node, b: Node} NAlt{a: Node, b: Node} NPlus{greedy: Bool, a: Node} NQuest{greedy: Bool, a: Node} NGroup{i: U32, a: Node}type Tok is Data: TAtom{n: Node} TOpen{cap: Bool} TClose{} TBar{} TRep{min: U32, max: Maybe<&2, U32>, greedy: Bool}def lit(+c: U32) -> Node: NSet{False{}, [Rng{c, c}]}def is_digit(+c: U32) -> Bool: U32.is_le(48, c) && U32.is_le(c, 57)def is_word(+c: U32) -> Bool: is_digit(c) || (U32.is_le(65, c) && U32.is_le(c, 90)) || (U32.is_le(97, c) && U32.is_le(c, 122)) || U32.is_eq(c, 95)def is_alnum(+c: U32) -> Bool: Bool.and(is_word(c), U32.is_ne(c, 95))# \d \w \s are ASCII, as in RE2.def perl.d() -> List<&2, Item>: [Rng{48, 57}]def perl.D() -> List<&2, Item>: [Rng{0, 47}, Rng{58, 1114111}]def perl.w() -> List<&2, Item>: [Rng{48, 57}, Rng{65, 90}, Rng{95, 95}, Rng{97, 122}]def perl.W() -> List<&2, Item>: [Rng{0, 47}, Rng{58, 64}, Rng{91, 94}, Rng{96, 96}, Rng{123, 1114111}]def perl.s() -> List<&2, Item>: [Rng{9, 10}, Rng{12, 13}, Rng{32, 32}]def perl.S() -> List<&2, Item>: [Rng{0, 8}, Rng{11, 11}, Rng{14, 31}, Rng{33, 1114111}]def cats() -> List<&2, String>: ["L", "Lu", "Ll", "Lt", "Lm", "Lo", "M", "Mn", "Mc", "Me", "N", "Nd", "Nl", "No", "P", "Pc", "Pd", "Ps", "Pe", "Pi", "Pf", "Po", "S", "Sm", "Sc", "Sk", "So", "Z", "Zs", "Zl", "Zp", "C", "Cc", "Cf", "Cs", "Co", "Cn"]# Escapes# -------type Esc is Data: EPoint{c: U32, rest: String} EItems{items: List<&2, Item>, rest: String} EAssert{k: U32, rest: String} EBad{}def prop.if(ok: Bool, neg: Bool, name: String, t: String) -> Esc: match ok: case True{}: EItems{[Prop{neg, name}], t} case False{}: EBad{}def prop.ok(neg: Bool, +name: String, t: String) -> Esc: prop.if(List.contains(~String, ~String.eq, cats(), name), neg, name, t)def prop.name(s: String, neg: Bool, acc: String) -> Esc: match s: case SNil{}: EBad{} case SCon{'}', t}: prop.ok(neg, String.reverse(acc), t) case SCon{c, t}: prop.name(t, neg, SCon{c, acc})# \pL or \p{Lu}; \P negates.def prop(neg: Bool, s: String) -> Esc: match s: case SNil{}: EBad{} case SCon{'{', t}: prop.name(t, neg, SNil{}) case SCon{c, t}: prop.ok(neg, SCon{c, SNil{}}, t)# An escaped letter or digit with no meaning is an error, as in RE2.def esc.other(alnum: Bool, +c: U32, t: String) -> Esc: match alnum: case True{}: EBad{} case False{}: EPoint{c, t}# The text after a backslash.def esc(s: String) -> Esc: match s: case SNil{}: EBad{} case SCon{'d', t}: EItems{perl.d(), t} case SCon{'D', t}: EItems{perl.D(), t} case SCon{'w', t}: EItems{perl.w(), t} case SCon{'W', t}: EItems{perl.W(), t} case SCon{'s', t}: EItems{perl.s(), t} case SCon{'S', t}: EItems{perl.S(), t} case SCon{'p', t}: prop(False{}, t) case SCon{'P', t}: prop(True{}, t) case SCon{'A', t}: EAssert{0, t} case SCon{'z', t}: EAssert{1, t} case SCon{'b', t}: EAssert{2, t} case SCon{'B', t}: EAssert{3, t} case SCon{'n', t}: EPoint{10, t} case SCon{'t', t}: EPoint{9, t} case SCon{'r', t}: EPoint{13, t} case SCon{'f', t}: EPoint{12, t} case SCon{'v', t}: EPoint{11, t} case SCon{Chr{+c}, t}: esc.other(is_alnum(c), c, t)# Classes# -------type Cs is Data: CsGo{s: String, first: Bool, items: List<&2, Item>} CsDone{items: List<&2, Item>, rest: String} CsFail{}def class.range(ok: Bool, +c: U32, +d: U32, u: String, items: List<&2, Item>) -> Cs: match ok: case True{}: CsGo{u, False{}, Rng{c, d} <> items} case False{}: CsFail{}def class.hi(e: Esc, +c: U32, items: List<&2, Item>) -> Cs: match e: case EPoint{+d, u}: class.range(U32.is_le(c, d), c, d, u, items) case EItems{xs, u}: CsFail{} case EAssert{k, u}: CsFail{} case EBad{}: CsFail{}# c is one member; a "-" and a code point after it make a range.def class.lo(+c: U32, t: String, items: List<&2, Item>) -> Cs: match t: case SCon{'-', SCon{']', u}}: CsDone{Rng{45, 45} <> Rng{c, c} <> items, u} case SCon{'-', SCon{'\\', u}}: class.hi(esc(u), c, items) case SCon{'-', SCon{Chr{+d}, u}}: class.range(U32.is_le(c, d), c, d, u, items) case _: CsGo{t, False{}, Rng{c, c} <> items}def class.esc(e: Esc, items: List<&2, Item>) -> Cs: match e: case EPoint{+c, t}: class.lo(c, t, items) case EItems{xs, t}: CsGo{t, False{}, List.append(&2, Item, xs, items)} case EAssert{k, t}: CsFail{} case EBad{}: CsFail{}# A "]" right after "[" or "[^" is a member.def class.step(s: String, first: Bool, items: List<&2, Item>) -> Cs: match s: case SNil{}: CsFail{} case SCon{']', t}: match first: case True{}: class.lo(93, t, items) case False{}: CsDone{items, t} case SCon{'\\', t}: class.esc(esc(t), items) case SCon{Chr{+c}, t}: class.lo(c, t, items)# fuel: every step eats at least one char.def class.run(fuel: Nat, st: Cs) -> Cs: match fuel: case 0n: CsFail{} case 1n+f: match st: case CsGo{s, first, items}: class.run(f, class.step(s, first, items)) case CsDone{items, rest}: CsDone{items, rest} case CsFail{}: CsFail{}def class(+s: String, first: Bool) -> Cs: class.run(Nat.add(String.length(s), 1n), CsGo{s, first, Nil{}})# Lexer# -----type Lx is Data: LGo{s: String, toks: List<&2, Tok>} LDone{toks: List<&2, Tok>} LFail{}# A run of decimal digits: its value (capped at 100000), its length, and the rest.type Num is Data: Num{v: U32, n: U32, rest: String}def num.add(+acc: U32, +c: U32) -> U32: Bool.pick(U32, U32.is_lt(acc, 100000), (acc * 10 + (c - 48) : U32), 100000)def num.go(t: String, +c: U32, +acc: U32, +n: U32, dig: Bool) -> Num: match t: case SNil{}: match dig: case True{}: Num{num.add(acc, c), (n + 1 : U32), SNil{}} case False{}: Num{acc, n, SCon{Chr{c}, SNil{}}} case SCon{Chr{+d}, u}: match dig: case True{}: num.go(u, d, num.add(acc, c), (n + 1 : U32), is_digit(d)) case False{}: Num{acc, n, SCon{Chr{c}, SCon{Chr{d}, u}}}def num(s: String) -> Num: match s: case SNil{}: Num{0, 0, SNil{}} case SCon{Chr{+c}, t}: num.go(t, c, 0, 0, is_digit(c))# A trailing "?" makes a repetition lazy.def lex.rep(+min: U32, max: Maybe<&2, U32>, t: String, toks: List<&2, Tok>) -> Lx: match t: case SCon{'?', u}: LGo{u, TRep{min, max, False{}} <> toks} case _: LGo{t, TRep{min, max, True{}} <> toks}def Num.n(m: Num) -> U32: Num{v, n, r} = m n# A "{" that does not start {n}, {n,} or {n,m} is a literal, as in RE2.def lex.brace.max(none: Bool, +min: U32, m: Num, orig: String, toks: List<&2, Tok>) -> Lx: match none: case True{}: LGo{orig, TAtom{lit(123)} <> toks} case False{}: Num{+v, n, r} = m match r: case SCon{'}', u}: lex.rep(min, Some{v}, u, toks) case _: LGo{orig, TAtom{lit(123)} <> toks}def lex.brace.min(none: Bool, m: Num, +orig: String, toks: List<&2, Tok>) -> Lx: match none: case True{}: LGo{orig, TAtom{lit(123)} <> toks} case False{}: Num{+v, n, r} = m match r: case SCon{'}', u}: lex.rep(v, Some{v}, u, toks) case SCon{',', SCon{'}', u}}: lex.rep(v, None{}, u, toks) case SCon{',', u}: +m2 = num(u) lex.brace.max(U32.is_eq(Num.n(m2), 0), v, m2, orig, toks) case _: LGo{orig, TAtom{lit(123)} <> toks}def lex.class(neg: Bool, r: Cs, toks: List<&2, Tok>) -> Lx: match r: case CsDone{items, rest}: LGo{rest, TAtom{NSet{neg, items}} <> toks} case CsGo{s, first, items}: LFail{} case CsFail{}: LFail{}def lex.esc(e: Esc, toks: List<&2, Tok>) -> Lx: match e: case EPoint{c, t}: LGo{t, TAtom{lit(c)} <> toks} case EItems{xs, t}: LGo{t, TAtom{NSet{False{}, xs}} <> toks} case EAssert{k, t}: LGo{t, TAtom{NAssert{k}} <> toks} case EBad{}: LFail{}def lex.step(s: String, toks: List<&2, Tok>) -> Lx: match s: case SNil{}: LDone{toks} case SCon{'\\', t}: lex.esc(esc(t), toks) case SCon{'[', SCon{'^', t}}: lex.class(True{}, class(t, True{}), toks) case SCon{'[', t}: lex.class(False{}, class(t, True{}), toks) case SCon{'(', SCon{'?', SCon{':', t}}}: LGo{t, TOpen{False{}} <> toks} case SCon{'(', SCon{'?', t}}: LFail{} case SCon{'(', t}: LGo{t, TOpen{True{}} <> toks} case SCon{')', t}: LGo{t, TClose{} <> toks} case SCon{'|', t}: LGo{t, TBar{} <> toks} case SCon{'*', t}: lex.rep(0, None{}, t, toks) case SCon{'+', t}: lex.rep(1, None{}, t, toks) case SCon{'?', t}: lex.rep(0, Some{1}, t, toks) case SCon{'{', +t}: +m = num(t) lex.brace.min(U32.is_eq(Num.n(m), 0), m, t, toks) case SCon{'.', t}: LGo{t, TAtom{NSet{True{}, [Rng{10, 10}]}} <> toks} case SCon{'^', t}: LGo{t, TAtom{NAssert{0}} <> toks} case SCon{'$', t}: LGo{t, TAtom{NAssert{1}} <> toks} case SCon{Chr{+c}, t}: LGo{t, TAtom{lit(c)} <> toks}# fuel: every step but the last eats at least one char.def lex(fuel: Nat, st: Lx) -> Maybe<&2, List<&2, Tok>>: match fuel: case 0n: None{} case 1n+f: match st: case LGo{s, toks}: lex(f, lex.step(s, toks)) case LDone{toks}: Some{List.reverse(&2, Tok, toks)} case LFail{}: None{}# Parser# ------# An open group: its capture index (None for (?:...)), and the enclosing alternatives and sequence.type Frame is Data: Frame{cap: Maybe<&2, U32>, alts: List<&2, Node>, cur: List<&2, Node>}# n: the next capture index. rep: the last token was a repetition. alts and cur are reversed.type Ps is Data: Ps{n: U32, rep: Bool, stack: List<&2, Frame>, alts: List<&2, Node>, cur: List<&2, Node>} PsFail{}def cat(a: Node, b: Node) -> Node: match a: case NEmpty{}: b case _: match b: case NEmpty{}: a case _: NCat{a, b}def seq.go(xs: List<&2, Node>, acc: Node) -> Node: match xs: case Nil{}: acc case Con{h, t}: seq.go(t, cat(h, acc))def seq(xs: List<&2, Node>) -> Node: seq.go(xs, NEmpty{})def alt.go(xs: List<&2, Node>, acc: Node) -> Node: match xs: case Nil{}: acc case Con{h, t}: alt.go(t, NAlt{h, acc})def group(cap: Maybe<&2, U32>, a: Node) -> Node: match cap: case None{}: a case Some{i}: NGroup{i, a}def rep.copies(k: Nat, +h: Node, acc: Node) -> Node: match k: case 0n: acc case 1n+p: rep.copies(p, h, cat(h, acc))def rep.opt(k: Nat, +g: Bool, +h: Node) -> Node: match k: case 0n: NEmpty{} case 1n+p: NQuest{g, cat(h, rep.opt(p, g, h))}# x* is (x+)?, so an empty x cannot loop; x{n,} is n-1 copies then x+; x{n,m} is n copies then (x(x...)?)?, as RE2 builds them.def rep.inf(k: Nat, +g: Bool, +h: Node) -> Node: match k: case 0n: NQuest{g, NPlus{g, h}} case 1n+p: rep.copies(p, h, NPlus{g, h})def rep.fin(max: Maybe<&2, U32>, +min: U32, +g: Bool, +h: Node) -> Node: match max: case None{}: rep.inf(U32.to_nat(min), g, h) case Some{m}: rep.copies(U32.to_nat(min), h, rep.opt(U32.to_nat((m - min : U32)), g, h))def rep(+h: Node, +min: U32, max: Maybe<&2, U32>, +g: Bool) -> Node: rep.fin(max, min, g, h)# Counts go up to 1000, and a repetition cannot repeat, as in RE2.def rep.ok(+min: U32, max: Maybe<&2, U32>) -> Bool: match max: case None{}: U32.is_le(min, 1000) case Some{+m}: U32.is_le(m, 1000) && U32.is_le(min, m)def parse.rep(ok: Bool, cur: List<&2, Node>, +min: U32, max: Maybe<&2, U32>, +g: Bool, +n: U32, stack: List<&2, Frame>, alts: List<&2, Node>) -> Ps: match ok: case False{}: PsFail{} case True{}: match cur: case Nil{}: PsFail{} case Con{h, t}: Ps{n, True{}, stack, alts, rep(h, min, max, g) <> t}def parse.open(cap: Bool, +n: U32, stack: List<&2, Frame>, alts: List<&2, Node>, cur: List<&2, Node>) -> Ps: match cap: case True{}: Ps{(n + 1 : U32), False{}, Frame{Some{n}, alts, cur} <> stack, Nil{}, Nil{}} case False{}: Ps{n, False{}, Frame{None{}, alts, cur} <> stack, Nil{}, Nil{}}def parse.close(stack: List<&2, Frame>, +n: U32, alts: List<&2, Node>, cur: List<&2, Node>) -> Ps: match stack: case Nil{}: PsFail{} case Con{Frame{cap, fa, fc}, up}: Ps{n, False{}, up, fa, group(cap, alt.go(alts, seq(cur))) <> fc}def parse.tok(tok: Tok, +n: U32, rep: Bool, stack: List<&2, Frame>, alts: List<&2, Node>, cur: List<&2, Node>) -> Ps: match tok: case TAtom{a}: Ps{n, False{}, stack, alts, a <> cur} case TRep{+min, +max, g}: parse.rep(Bool.and(Bool.not(rep), rep.ok(min, max)), cur, min, max, g, n, stack, alts) case TOpen{cap}: parse.open(cap, n, stack, alts, cur) case TClose{}: parse.close(stack, n, alts, cur) case TBar{}: Ps{n, False{}, stack, seq(cur) <> alts, Nil{}}def parse.step(st: Ps, tok: Tok) -> Ps: match st: case PsFail{}: PsFail{} case Ps{n, rep, stack, alts, cur}: parse.tok(tok, n, rep, stack, alts, cur)def parse(toks: List<&2, Tok>, st: Ps) -> Ps: match toks: case Nil{}: st case Con{tok, t}: parse(t, parse.step(st, tok))# Compiler# --------type Inst is Data: ISet{neg: Bool, items: List<&2, Item>} IAssert{k: U32} ISplit{x: U32, y: U32} IJmp{x: U32} ISave{k: U32} IMatch{}def size(n: Node) -> U32: match n: case NEmpty{}: 0 case NSet{neg, items}: 1 case NAssert{k}: 1 case NCat{a, b}: (size(a) + size(b) : U32) case NAlt{a, b}: (2 + size(a) + size(b) : U32) case NPlus{g, a}: (1 + size(a) : U32) case NQuest{g, a}: (1 + size(a) : U32) case NGroup{i, a}: (2 + size(a) : U32)# The instructions of n, placed at pc, in front of rest. ISplit tries x first.def emit(n: Node, +pc: U32, rest: List<&2, Inst>) -> List<&2, Inst>: match n: case NEmpty{}: rest case NSet{neg, items}: ISet{neg, items} <> rest case NAssert{k}: IAssert{k} <> rest case NCat{+a, b}: emit(a, pc, emit(b, (pc + size(a) : U32), rest)) case NAlt{+a, +b}: +j = (pc + 1 + size(a) : U32) ISplit{(pc + 1 : U32), (j + 1 : U32)} <> emit(a, (pc + 1 : U32), IJmp{(j + 1 + size(b) : U32)} <> emit(b, (j + 1 : U32), rest)) case NPlus{+g, +a}: +out = (pc + 1 + size(a) : U32) emit(a, pc, ISplit{Bool.pick(U32, g, pc, out), Bool.pick(U32, g, out, pc)} <> rest) case NQuest{+g, +a}: +out = (pc + 1 + size(a) : U32) ISplit{Bool.pick(U32, g, (pc + 1 : U32), out), Bool.pick(U32, g, out, (pc + 1 : U32))} <> emit(a, (pc + 1 : U32), rest) case NGroup{+i, a}: ISave{(2 * i : U32)} <> emit(a, (pc + 1 : U32), ISave{(2 * i + 1 : U32)} <> rest)# A binary trie keyed by n >= 1: the path is the bits of n below its top bit, low bit# first, so key n costs log2(n) steps and small keys stay near the root.type Trie<-V: Data> is Data: TTip{} TNode{val: Maybe<&2, V>, lo: Trie<V>, hi: Trie<V>}# here: n is 1. left: n is even.def trie.get(-V: Data, t: Trie<V>, here: Bool, left: Bool, +n: U32) -> Maybe<&2, V>: match t: case TTip{}: None{} case TNode{v, lo, hi}: match here: case True{}: v case False{}: match left: case True{}: trie.get(V, lo, U32.is_eq(U32.shr(n), 1), U32.is_even(U32.shr(n)), U32.shr(n)) case False{}: trie.get(V, hi, U32.is_eq(U32.shr(n), 1), U32.is_even(U32.shr(n)), U32.shr(n))# fuel: a U32 key has at most 32 bits.def trie.put(-V: Data, fuel: Nat, t: Trie<V>, here: Bool, left: Bool, +n: U32, v: V) -> Trie<V>: match fuel: case 0n: t case 1n+f: match t: case TNode{x, lo, hi}: match here: case True{}: TNode{Some{v}, lo, hi} case False{}: match left: case True{}: TNode{x, trie.put(V, f, lo, U32.is_eq(U32.shr(n), 1), U32.is_even(U32.shr(n)), U32.shr(n), v), hi} case False{}: TNode{x, lo, trie.put(V, f, hi, U32.is_eq(U32.shr(n), 1), U32.is_even(U32.shr(n)), U32.shr(n), v)} case TTip{}: match here: case True{}: TNode{Some{v}, TTip{}, TTip{}} case False{}: match left: case True{}: TNode{None{}, trie.put(V, f, TTip{}, U32.is_eq(U32.shr(n), 1), U32.is_even(U32.shr(n)), U32.shr(n), v), TTip{}} case False{}: TNode{None{}, TTip{}, trie.put(V, f, TTip{}, U32.is_eq(U32.shr(n), 1), U32.is_even(U32.shr(n)), U32.shr(n), v)}# The value at key k, stored as n = k + 1.def trie.at(-V: Data, t: Trie<V>, +k: U32) -> Maybe<&2, V>: +n = (k + 1 : U32) trie.get(V, t, U32.is_eq(n, 1), U32.is_even(n), n)def trie.set(-V: Data, t: Trie<V>, +k: U32, v: V) -> Trie<V>: +n = (k + 1 : U32) trie.put(V, 32n, t, U32.is_eq(n, 1), U32.is_even(n), n, v)def trie.from(-V: Data, xs: List<&2, V>, +k: U32, t: Trie<V>) -> Trie<V>: match xs: case Nil{}: t case Con{h, r}: trie.from(V, r, (k + 1 : U32), trie.set(V, t, k, h))# prog: the instructions by pc; fuel: enough steps for one closure; slots: two per group, group 0 included.type Regex is Data: Regex{prog: Trie<Inst>, fuel: Nat, slots: Nat}def build(+node: Node, +n: U32) -> Regex: +insts = {ISave{0} <> emit(node, 1, [ISave{1}, IMatch{}]) : List<&2, Inst>} Regex{trie.from(Inst, insts, 0, TTip{}), Nat.add(Nat.mul(3n, List.length(&2, Inst, insts)), 2n), U32.to_nat((2 * n : U32))}def compile.fin(st: Ps) -> Maybe<&2, Regex>: match st: case PsFail{}: None{} case Ps{n, rep, stack, alts, cur}: match stack: case Nil{}: Some{build(alt.go(alts, seq(cur)), n)} case Con{f, up}: None{}def compile.parse(toks: Maybe<&2, List<&2, Tok>>) -> Maybe<&2, Regex>: match toks: case None{}: None{} case Some{ts}: compile.fin(parse(ts, Ps{1, False{}, Nil{}, Nil{}, Nil{}}))# The pattern, or None for a syntax error.def compile(+pat: String) -> Maybe<&2, Regex>: compile.parse(lex(Nat.add(String.length(pat), 2n), LGo{pat, Nil{}}))# Matcher# -------def item.has(i: Item, +c: U32) -> Bool: match i: case Rng{+lo, +hi}: U32.is_le(lo, c) && U32.is_le(c, hi) case Prop{neg, name}: Bool.xor(neg, String.starts_with(U.category(Chr{c}), name))def items.has(xs: List<&2, Item>, +c: U32) -> Bool: match xs: case Nil{}: False{} case Con{h, t}: item.has(h, c) || items.has(t, c)def word(m: Maybe<&2, Char>) -> Bool: match m: case None{}: False{} case Some{Chr{+c}}: is_word(c)def assert.ok(k: U32, +prev: Maybe<&2, Char>, +next: Maybe<&2, Char>) -> Bool: match k: case 0: Maybe.is_none(&2, Char, prev) case 1: Maybe.is_none(&2, Char, next) case 2: Bool.xor(word(prev), word(next)) case _: Bool.not(Bool.xor(word(prev), word(next)))# A thread: its pc and its capture slots.type Th is Data: Th{pc: U32, caps: List<&2, Maybe<&2, U32>>}# The epsilon closure as a depth-first walk: stack is the work left, seen the pcs# visited at this position, out the threads that wait on a char or match (reversed).type Cl is Data: Cl{stack: List<&2, Th>, seen: Trie<Unit>, out: List<&2, Th>}def close.assert(ok: Bool, +pc: U32, caps: List<&2, Maybe<&2, U32>>, stack: List<&2, Th>, seen: Trie<Unit>, out: List<&2, Th>) -> Cl: match ok: case True{}: Cl{Th{(pc + 1 : U32), caps} <> stack, seen, out} case False{}: Cl{stack, seen, out}def close.inst(i: Maybe<&2, Inst>, +pc: U32, +caps: List<&2, Maybe<&2, U32>>, stack: List<&2, Th>, seen: Trie<Unit>, out: List<&2, Th>, +pos: U32, +prev: Maybe<&2, Char>, +next: Maybe<&2, Char>) -> Cl: match i: case None{}: Cl{stack, seen, out} case Some{IJmp{x}}: Cl{Th{x, caps} <> stack, seen, out} case Some{ISplit{x, y}}: Cl{Th{x, caps} <> Th{y, caps} <> stack, seen, out} case Some{ISave{k}}: Cl{Th{(pc + 1 : U32), List.set(&2, Maybe<&2, U32>, caps, U32.to_nat(k), Some{pos})} <> stack, seen, out} case Some{IAssert{k}}: close.assert(assert.ok(k, prev, next), pc, caps, stack, seen, out) case Some{ISet{neg, items}}: Cl{stack, seen, Th{pc, caps} <> out} case Some{IMatch{}}: Cl{stack, seen, Th{pc, caps} <> out}# ponytail: trie lookup and membership cost O(log m) per thread step, so a char costs# O(m log m) for m instructions; a sparse set over an Array would make a step O(1).def close.seen(hit: Bool, +prog: Trie<Inst>, +pc: U32, caps: List<&2, Maybe<&2, U32>>, stack: List<&2, Th>, seen: Trie<Unit>, out: List<&2, Th>, +pos: U32, +prev: Maybe<&2, Char>, +next: Maybe<&2, Char>) -> Cl: match hit: case True{}: Cl{stack, seen, out} case False{}: close.inst(trie.at(Inst, prog, pc), pc, caps, stack, trie.set(Unit, seen, pc, Unit{}), out, pos, prev, next)def close.step(th: Th, stack: List<&2, Th>, +seen: Trie<Unit>, out: List<&2, Th>, +prog: Trie<Inst>, +pos: U32, +prev: Maybe<&2, Char>, +next: Maybe<&2, Char>) -> Cl: Th{+pc, caps} = th close.seen(Maybe.is_some(&2, Unit, trie.at(Unit, seen, pc)), prog, pc, caps, stack, seen, out, pos, prev, next)# fuel: each pc expands once and pushes at most two threads.def close(fuel: Nat, +prog: Trie<Inst>, +pos: U32, +prev: Maybe<&2, Char>, +next: Maybe<&2, Char>, st: Cl) -> List<&2, Th>: match fuel: case 0n: Cl{stack, seen, out} = st List.reverse(&2, Th, out) case 1n+f: match st: case Cl{Nil{}, seen, out}: List.reverse(&2, Th, out) case Cl{Con{th, t}, seen, out}: close(f, prog, pos, prev, next, close.step(th, t, seen, out, prog, pos, prev, next))# A scan of the threads at one char, in priority order: items are the threads that# step past it (reversed), best the latest match. A match drops every later thread.type Sc is Data: Sc{items: List<&2, Th>, best: Maybe<&2, List<&2, Maybe<&2, U32>>>, stop: Bool}def scan.set(hit: Bool, +pc: U32, caps: List<&2, Maybe<&2, U32>>, items: List<&2, Th>, best: Maybe<&2, List<&2, Maybe<&2, U32>>>) -> Sc: match hit: case True{}: Sc{Th{(pc + 1 : U32), caps} <> items, best, False{}} case False{}: Sc{items, best, False{}}def scan.char(c: Maybe<&2, Char>, neg: Bool, set: List<&2, Item>, +pc: U32, caps: List<&2, Maybe<&2, U32>>, items: List<&2, Th>, best: Maybe<&2, List<&2, Maybe<&2, U32>>>) -> Sc: match c: case None{}: Sc{items, best, False{}} case Some{Chr{+x}}: scan.set(Bool.xor(neg, items.has(set, x)), pc, caps, items, best)# any: only whether a match exists counts, so a match also drops the earlier threads.def scan.hit(any: Bool, caps: List<&2, Maybe<&2, U32>>, items: List<&2, Th>) -> Sc: match any: case True{}: Sc{Nil{}, Some{caps}, True{}} case False{}: Sc{items, Some{caps}, True{}}def scan.inst(i: Maybe<&2, Inst>, c: Maybe<&2, Char>, +any: Bool, +pc: U32, caps: List<&2, Maybe<&2, U32>>, items: List<&2, Th>, best: Maybe<&2, List<&2, Maybe<&2, U32>>>) -> Sc: match i: case Some{IMatch{}}: scan.hit(any, caps, items) case Some{ISet{neg, set}}: scan.char(c, neg, set, pc, caps, items, best) case _: Sc{items, best, False{}}def scan.go(stop: Bool, th: Th, +prog: Trie<Inst>, c: Maybe<&2, Char>, +any: Bool, items: List<&2, Th>, best: Maybe<&2, List<&2, Maybe<&2, U32>>>) -> Sc: match stop: case True{}: Sc{items, best, True{}} case False{}: Th{+pc, caps} = th scan.inst(trie.at(Inst, prog, pc), c, any, pc, caps, items, best)def scan.step(st: Sc, th: Th, +prog: Trie<Inst>, c: Maybe<&2, Char>, +any: Bool) -> Sc: Sc{items, best, stop} = st scan.go(stop, th, prog, c, any, items, best)def scan(xs: List<&2, Th>, +prog: Trie<Inst>, +c: Maybe<&2, Char>, +any: Bool, st: Sc) -> Sc: match xs: case Nil{}: st case Con{th, t}: scan(t, prog, c, any, scan.step(st, th, prog, c, any))# The live threads and the best match so far.type Vm is Data: Vm{ths: List<&2, Th>, best: Maybe<&2, List<&2, Maybe<&2, U32>>>}# Until a match is found, a new thread starts at each position, below every other.def seed(best: Maybe<&2, List<&2, Maybe<&2, U32>>>, xs: List<&2, Th>, init: List<&2, Maybe<&2, U32>>) -> List<&2, Th>: match best: case None{}: List.append(&2, Th, xs, [Th{0, init}]) case Some{b}: xsdef run.close(sc: Sc, +prog: Trie<Inst>, +fuel: Nat, +init: List<&2, Maybe<&2, U32>>, +pos: U32, +prev: Maybe<&2, Char>, +next: Maybe<&2, Char>) -> Vm: Sc{items, +best, stop} = sc Vm{close(fuel, prog, pos, prev, next, Cl{seed(best, List.reverse(&2, Th, items), init), TTip{}, Nil{}}), best}def run.step(st: Vm, +prog: Trie<Inst>, +fuel: Nat, +init: List<&2, Maybe<&2, U32>>, +any: Bool, +pos: U32, +c: Char, +next: Maybe<&2, Char>) -> Vm: Vm{ths, best} = st run.close(scan(ths, prog, Some{c}, any, Sc{Nil{}, best, False{}}), prog, fuel, init, pos, Some{c}, next)def run.end(sc: Sc) -> Maybe<&2, List<&2, Maybe<&2, U32>>>: Sc{items, best, stop} = sc best# pos: the position of s's head. Once a match exists and no thread is live, the rest of s cannot change it.def run(s: String, +prog: Trie<Inst>, +fuel: Nat, +init: List<&2, Maybe<&2, U32>>, +any: Bool, +pos: U32, st: Vm) -> Maybe<&2, List<&2, Maybe<&2, U32>>>: match s: case SNil{}: Vm{ths, best} = st run.end(scan(ths, prog, None{}, any, Sc{Nil{}, best, False{}})) case SCon{+c, +t}: match st: case Vm{Nil{}, Some{b}}: Some{b} case Vm{ths, best}: +p = (pos + 1 : U32) run(t, prog, fuel, init, any, p, run.step(Vm{ths, best}, prog, fuel, init, any, p, c, String.get(t, 0n)))type Span is Data: Span{start: U32, end: U32}def spans(caps: List<&2, Maybe<&2, U32>>) -> List<&2, Maybe<&2, Span>>: match caps: case Con{Some{a}, Con{Some{b}, t}}: Some{Span{a, b}} <> spans(t) case Con{x, Con{y, t}}: None{} <> spans(t) case _: Nil{}def find.spans(m: Maybe<&2, List<&2, Maybe<&2, U32>>>) -> Maybe<&2, List<&2, Maybe<&2, Span>>>: match m: case None{}: None{} case Some{caps}: Some{spans(caps)}# slots: capture slots to keep; is_match keeps none, so each ISave is free.def exec(re: Regex, +s: String, +any: Bool) -> Maybe<&2, List<&2, Maybe<&2, U32>>>: Regex{+prog, +fuel, +slots} = re +init = List.replicate(Maybe<&2, U32>, Bool.pick(Nat, any, 0n, slots), None{}) run(s, prog, fuel, init, any, 0, Vm{close(fuel, prog, 0, None{}, String.get(s, 0n), Cl{[Th{0, init}], TTip{}, Nil{}}), None{}})# The leftmost match in s: the span of group 0, then of each group; None for a group that did not take part.def find(re: Regex, +s: String) -> Maybe<&2, List<&2, Maybe<&2, Span>>>: find.spans(exec(re, s, False{}))# Stops at the first match of any priority and records no captures.def is_match(re: Regex, +s: String) -> Bool: Maybe.is_some(&2, List<&2, Maybe<&2, U32>>, exec(re, s, True{}))